Texas Instruments (TI) Calculators for Probability Distributions

You may use any of these TI calculators:
TI-83 Plus
TI-84 Plus series
TI-Nspire CX series
TI-89 Titanium
TI-73 Explorer


Notable Notes
(1.) To find the probability of any probability distribution, use the distribution function DISTR
Because this is in blue color, it can be assessed after 2ND function button is pressed (because the 2ND function button is blue)



(2.) For Normal Distribution:
(a.) To find the area or percentage or probability: (i.) less than or equal to a certain value (at most the certain value)
(ii.) more than or equal to a certain value (at least the certain value)
(iii.) between two values
(iv.) away from two values
Use the normalcdf (Normal Cumulative Distribution) function



(b.) To find the area or percentage or probability: less than or equal to a certain value (at most the certain value):
(i.) set the lower: −1000000
(ii.) set the upper: certain value





(c.) To find the area or percentage or probability: greater than or equal to a certain value (at least the certain value):
(i.) set the lower: certain value
(ii.) set the upper: 1000000



(d.) To find the area or percentage or probability between two values:
(i.) set the lower: first value
(ii.) set the upper: second value

(e.) To find the area or percentage or probability away from two values:
(i.) set the lower: −1000000
(ii.) set the upper: first value
Added to
(iii.) set the lower: second value
(iv.) set the upper: 1000000

(3.) To find the inverse of any probability distribution, use the distribution function DISTR
Because this is in blue color, it can be assessed after 2ND function button is pressed (because the 2ND function button is blue)



(4.)

Let us do some examples.
NOTE: Please begin from the first example. Do not skip.

Normal Distribution Application
(1.) Find the probability that a z-score will be 1.54 or less.
(Round to four decimal places as needed.)

Show/Hide Answer

(a.) The graph that shows the probability that a z-score is 1.54 or less is option D.


(b.) 1.54 = 1.5 (vertical); 0.04 (horizontal)

First Approach: Left-Shaded Area


The probability that a z-score will be 1.54 or less = P(z ≤ 1.54)
= 0.93822 ≈ 0.9382

Second Approach: Center-Shaded Area


The probability that a z-score will be 1.54 or less
= P(z ≤ 1.54)
= 0.5 + 0.43822
= 0.93822 ≈ 0.9382

Third Approach: Texas Instruments (TI) technology
Please see screenshots below.
The probability that a z-score will be 1.54 or less
= 0.9382198075 ≈ 0.9382

Normal Distribution Application
(2.) Find the probability that a z-score will be 1.54 or more.
(Round to four decimal places as needed.)

Show/Hide Answer

(c.) The graph that shows the probability that a z-score is 1.54 or more is option B.


(d.) First Approach: Left-Shaded Area
The probability that a z-score will be 1.54 or more
= P(z ≥ 1.54)
= 1 − 0.93822
= 0.06178 ≈ 0.0618

Second Approach: Center-Shaded Area


The probability that a z-score will be 1.54 or more
= P(z ≥ 1.54)
= 0.5 − 0.43822
= 0.06178 ≈ 0.0618

Third Approach: Texas Instruments (TI) technology
Please see screenshots below.
The probability that a z-score will be 1.54 or more
= 0.0617801925 ≈ 0.0618

Normal Distribution Application
(3.) Find the probability that a z-score will be between −1.5 and −1.05.
(Round to four decimal places as needed.)

Show/Hide Answer

(e.) The graph that shows the probability that a z-score is between −1.5 and −1.05 is option A.


(f.) −1.5 = −1.5 (vertical); 0.00 (horizontal)
−1.05 = −1.0 (vertical); 0.05 (horizontal)

First Approach: Left-Shaded Area


The probability that a z-score is between −1.5 and −1.05
= P(−1.5 ≤ z ≤ −1.05)
= P(z ≤ −1.05) - P(z ≤ −1.5)
= 0.14686 − 0.06681
= 0.08005 ≈ 0.0801

Second Approach: Center-Shaded Area


The probability that a z-score is between −1.5 and −1.05
= P(−1.5 ≤ z ≤ −1.05)
= P(0 ≤ z ≤ −1.5) − = P(0 ≤ z ≤ −1.05)...symmetrical
= 0.43319 − 0.35314
= 0.08005 ≈ 0.0801

Third Approach: Texas Instruments (TI) technology
Please see screenshots below.
The probability that a z-score is between −1.5 and −1.05
= 0.080018519 ≈ 0.0801